Velikaya began fencing at the age of 13 after her elder brother took up the sport. Her first coach was Valery Dyakokin. She missed a place in the 2004 Olympics in Athens by one point. She placed fourth in the 2008 Beijing Games after losing to Rebecca Ward by one point in the bronze medal match. On 12 October 2011, she became the World Champion after beating two-time Olympic champion Mariel Zagunis in the final. One year after, she took part in the Summer Olympics in London, where she advanced to finals after defeating Olga Kharlan of Ukraine. She lost however to South Korea's Kim Ji-yeon and captured silver. After the Olympics Velikaya took a break in her career. She gave birth to Oleg, with Olympic wrestler Aleksey Mishin. She came back to international competition in March 2014 at the Antalya World Cup, where she was defeated in the second round by Hungary's Anna Várhelyi. At the European Championships in Strasbourg, she was stopped in the second round again, this time by Italy's Rossella Gregorio. In the team event, Russia defeated Germany and Hungary to meet France in the final. After being led 30–35 Russia overcame France in the last two relays to win the gold medal. At the World Championships in Kazan Velikaya made her way to the quarter-finals, where she met reigning World champion Olga Kharlan of Ukraine. After a good beginning Velikaya could not prevent Kharlan's comeback and was defeated 9–15. She was however pleased by her return to form. In the team event, Russia overcame Canada easily in the round of 16 and met France in the quarter-finals. Surprised by France's outright attack, Russia did not manage to regain control and suffered a shock 41–45 defeat. They entered placement rounds and finished 5th after prevailing over South Korea and Poland. In the 2014–15 season, Velikaya won the first event held in Cancún after defeating France's Charlotte Lembach in the final. She placed second with Russia in the team event. In Orléans, Velikaya put an end to the invincibility of the world no.1 Olga Kharlan, who had not taken part in the Cancún tournament. Velikaya proceeded to the final where she defeated Italy's Rossella Gregorio and earned her second gold medal in a row. In the team event, Russia stormed through the competition and saw off the United States in the final to win team gold. Velikaya reached again the final in the New York Grand Prix. She met Kharlan, who defeated her 15–12, dooming her the silver medal. The same scenario played out in Athens at the first World Cup event of 2015, Velikaya losing only by a single hit that time. In the team event, Russia fenced Ukraine in the final. After a tight match Russia lost ground in the penultimate relay, which ended on 33–40. Velikaya lost 2–5 the final relay against Kharlan and came away with a second silver medal. She took her revenge at the Ghent World Cup, defeating Kharlan 15–3 in the semi-finals, then Zagunis 15–10 in the final, to take her third gold medal of the season. This result caused her to jump to the third place in World rankings. Velikaya qualified for the 2016 Summer Olympics in Rio de Janeiro alongside her teammates Yana Egorian and Ekaterina Dyachenko. In women's sabre in the table of 32 she defeated Bogna Jóźwiak from Poland. In the table of 16, quarter-finals and semi-finals, Velikaya prevailed over Charlotte Lembach, Cécilia Berder and Manon Brunet of France, respectively. She eventually lost 14–15 to her teammate Yana Egorian in the finals, winning her second consecutive silver medal at the Olympics in the individual women's sabre. Velikaya finally managed to claim the Olympic gold a few days later in the team event. Russia defeated Mexico in the quarter-finals, prevailed over the USA in the semi-finals and met the Ukrainian in the final. Velikaya and her teammates, including Yuliya Gavrilova, came away with the gold medal, defeating Ukraine 45–30. Velikaya was ranked Nr. 1 in the women's sabre for the most of 2016. She was succeeded by Yana Egorian as the new No. 1. Velikaya finished 2016 as the world's No. 3. On 17 November 2016, Velikaya was elected the head of the Russian Olympic Committee Athletes' Commission. During her tenure on the committee, Velikaya has spearheaded the response to the Russian doping scandal, including holding public events in person and online to address necessary changes to bring Team Russiaback in line with Olympic doping guidelines.
*1st class – for outstanding contribution to the development of physical culture and sports, high achievements at the Games of the 30th Olympic Games in London, United Kingdom.
Velikaya is married to 2004 Olympic Champion wrestler, Aleksey Mishin. They have two child together, a son, named Oleg, born on 30 November 2013, and a girl named Zoya, born in 2018.
At the age of 15, Sofya moved from the small town of Alma-Ata in Kazakhstan to Moscow to train in fencing.
Prior to starting fencing, she played piano as a child.
Her surname, Velikaya, means "great" or "grand" in Russian.